A208253 Number of n X 3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

5, 96, 2040, 43344, 920928, 19566912, 415737216, 8833148160, 187677464064, 3987573838848, 84723785029632, 1800122089230336, 38247105402593280, 812634365429366784, 17266002353004576768, 366849901919230820352

Offset

1,1

Comments

Column 3 of A208258.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 22*a(n-1) - 16*a(n-2) for n>3.

Conjectures from Colin Barker, Jun 29 2018: (Start)

G.f.: x*(1 - 2*x)*(5 - 4*x) / (1 - 22*x + 16*x^2).

a(n) = (1/32)*sqrt(3/35)*((11-sqrt(105))^n*(-13+sqrt(105)) + (11+sqrt(105))^n*(13+sqrt(105))) for n>1.

(End)

Example

Some solutions for n=4:
..0..0..1....0..0..0....0..1..0....0..0..1....0..0..0....0..1..2....0..0..1
..2..0..0....0..1..2....0..1..1....2..0..2....1..2..1....1..2..0....1..1..2
..2..0..1....2..0..0....1..0..2....0..2..0....0..2..2....0..1..0....1..0..1
..2..2..2....1..0..1....1..2..0....2..0..2....0..0..2....2..0..1....2..1..2

Crossrefs

Cf. A208258.

Sequence in context: A266245 A194616 A285367 * A284664 A194609 A139950

Adjacent sequences: A208250 A208251 A208252 * A208254 A208255 A208256

Keyword

nonn

Author

R. H. Hardin, Feb 24 2012

Status

approved